A pentagon has actually 5 sides, and can be made indigenous three triangles, therefore you know what ...
You are watching: If the sum of the interior angles of a polygon is 540 then how many sides does the polygon have
... Its interior angles add up to 3 × 180° = 540°
And as soon as it is regular (all angles the same), climate each edge is 540° / 5 = 108°
(Exercise: make certain each triangle below adds up to 180°, and also check the the pentagon"s internal angles include up to 540°)
The inner Angles the a Pentagon include up come 540°
The basic Rule
Each time we include a next (triangle come quadrilateral, square to pentagon, etc), we add another 180° to the total:
|If that is a Regular Polygon (all sides room equal, all angles room equal)|
|Heptagon (or Septagon)||7||900°||128.57...°|
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|Any Polygon||n||(n−2) × 180°||(n−2) × 180° / n|
So the general dominance is:
Sum of internal Angles = (n−2) × 180°
Each angle (of a continuous Polygon) = (n−2) × 180° / n
Perhaps an example will help:
Example: What about a constant Decagon (10 sides) ?
Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
And because that a regular Decagon:
Each interior angle = 1440°/10 = 144°
Note: inner Angles space sometimes called "Internal Angles"
interior Angles Exterior Angles levels (Angle) 2D forms Triangles square Geometry Index